共查询到20条相似文献,搜索用时 46 毫秒
1.
Guido M. Pinkernell 《Journal of Geometry》1996,55(1-2):141-161
The subject of this paper are two pencils of cubic curves that are the result of certain geometrical constructions in the triangle plane. One of them turns out to be the probably most significant pencil of anallagmatic cubics that are associated with triangle geometry. Both contain virtually all important single cubics, and other well known curves appear closely connected with them.Dedicated to Professor T.G. Ostrom on the occasion of his 80th birthday 相似文献
2.
Chun Shen 《Mathematical Methods in the Applied Sciences》2020,43(6):3673-3688
The formation of vacuum state and delta shock wave are observed and studied in the limits of Riemann solutions for the one-dimensional isentropic drift-flux model of compressible two-phase flows by letting the pressure in the mixture momentum equation tend to zero. It is shown that the Riemann solution containing two rarefaction waves and one contact discontinuity turns out to be the solution containing two contact discontinuities with the vacuum state between them in the limiting situation. By comparison, it is also proved rigorously in the sense of distributions that the Riemann solution containing two shock waves and one contact discontinuity converges to a delta shock wave solution under this vanishing pressure limit. 相似文献
3.
The problem of producing medium- to long-term forecasts of the market for business telephones is examined. Growth curves are generally appropriate for forecasting developing markets. However, this market is particularly sensitive to the state of business confidence and the feasibility of incorporating explanatory economic variables into the forecasting model is investigated. Three different model types are compared: growth curves with a fixed saturation level, multivariate linear models and growth curves with saturation levels determined by explanatory variables. The initial promise of models using explanatory variables is considerably diminished, once forecast rather than actual values of these variables are used. The market development model implicit in the growth curve is shown to be more robust than the linear model. Although the variable saturation level growth curve grants more insight into the maturity of the market, it does not produce significantly better forecasts than that with the fixed saturation level. 相似文献
4.
Robert S. Maier 《manuscripta mathematica》2011,134(1-2):1-42
A unified treatment is given of low-weight modular forms on ?? 0(N), N = 2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under ?? 0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard?CFuchs equations of triangle subgroups of PSL(2, R), which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with ??(1) is treated. 相似文献
5.
We study certain group actions on triangle buildings and their boundaries and some von Neumann algebras which can be constructed from them. In particular, for buildings of orderq?3 certain natural actions on the boundary are hyperfinite of type III1/q2. 相似文献
6.
Sam Northshield 《Journal of Mathematical Analysis and Applications》2011,374(2):385-393
Sums across the rows of Pascal's triangle yield n2 while certain diagonal sums yield the Fibonacci numbers which are asymptotic to ?n where ? is the golden ratio. Sums across other diagonals yield quantities asymptotic to cn where c depends on the directions of the diagonals. We generalize this to the continuous case. Using the gamma function, we generalize the binomial coefficients to real variables and thus form a generalization of Pascal's triangle. Integration over various families of lines and curves yields quantities asymptotic to cx where c is determined by the family and x is a parameter. Finally, we revisit the discrete case to get results on sums along curves. 相似文献
7.
This paper is concerned with the design of incomplete equations of state for a two-phase flow with phase transition that are specific to the low Mach number regime. It makes use of the fact that the thermodynamic pressure has small variations in this regime. These equations of state supplement the 2D Lmnc model introduced in previous works.Our innovative strategy relies on tabulated values and is proven to satisfy crucial thermodynamic requirements such as positivity, monotonicity and continuity. In particular, saturation values are exact. This procedure is assessed by means of analytical steady solutions and comparisons with standard analytical equations of state, and shows a great improvement in accuracy. 相似文献
8.
Chenxi Wu 《Geometriae Dedicata》2017,187(1):107-121
We calculate the area of the smallest triangle and the area of the smallest virtual triangle for many known lattice surfaces. We show that our list of the lattice surfaces for which the area of the smallest virtual triangle greater than \(1\over 20\) is complete. In particular, this means that there are no new lattice surfaces for which the area of the smallest virtual triangle is greater than .05. Our method follows an algorithm described by Smillie and Weiss and improves on it in certain respects. 相似文献
9.
10.
《代数通讯》2013,41(7):2505-2526
Abstract We study the quotient of a free product of groups by the normal closure of a word that is contained in a certain type of 2-generator subgroup, and hence can be expressed in the form of a pushout involving a generalized triangle group. Using the theory of generalized triangle groups, we extend the range of conditions under which a number of results for one-relator products of groups, such as the Freiheitssatz and the solubility of the word problem, are known to hold. 相似文献
11.
Keiji Nishioka 《manuscripta mathematica》1990,66(1):341-349
It is proved that a certain type of third order algebraic differential equations defined over ℂ which are satisfied by Schwarz
triangle functions, cannot be reduced to first order. 相似文献
12.
There are many interesting cubic curves which arise from the geometry of the triangle. In particular, those which are invariant under the operation of isogonal conjugacy have attracted much attention, and a class of these is here investigated by a variety of methods. 相似文献
13.
Bjö rn Sjö green Katarina Gustavsson Reynir Levi Gudmundsson. 《Mathematics of Computation》2007,76(260):1925-1940
We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is well-posed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exist at certain times. We prove that the model problem has a smooth solution for bounded times.
14.
15.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(9):1047-1052
Let p be a prime number. Associated to every elliptic curve E over Qp there is a local root number Wp(E) = ±1, constructed from the local epsilon factors of Deligne. This sign is already known when p > 3, and also, in certain cases, when p = 2 or 3. In this Note, we give the value of W2 or W3 in all cases. Concerning W3, for our results to be valid, we have to assume that a certain (finite) number of auxiliary elliptic curves over Q are Weil curves. 相似文献
16.
《Journal of Combinatorial Theory, Series A》1987,46(2):183-211
We determine the number of projectively inequivalent nonsingular plane cubic curves over a finite field Fq with a fixed number of points defined over Fq. We count these curves by counting elliptic curves over Fq together with a rational point which is annihilated by 3, up to a certain equivalence relation. 相似文献
17.
1.引言多孔介质二相驱动问题的数学模型是偶合的非线性偏微分方程组的初边值问题.该问题可转化为压力方程和浓度方程[1-4].浓度方程一般是对流占优的对流扩散方程,它的对流速度依赖于比浓度方程的扩散系数大得多的Farcy速度.因此Darcy速度的求解精度直接影响着浓度的求解精度.为了提高速度的求解精度,70年代P.A.Raviat和J.M.Thomas提出混合有限元方法[5].J.DouglasJr,T.F.Russell,R.E.Ewing,M.F.Wheeler[1]-[4],[9],[12]袁… 相似文献
18.
We study the asymptotic behavior of the zeros of certain families of 3F2 functions. Classical tools are used to analyse the asymptotic behavior of the zeros of the polynomial
In addition, families of 3F2 functions that are connected in a formulaic sense with Gauss hypergeometric polynomials of the form
and
are investigated. Numerical evidence of the clustering o zeros on certain curves is generated by Mathematica. 相似文献
19.
Answering a question of H. Harborth, for any given a
1,...,a
n
> 0, satisfying
we determine the infimum of the areas of the simple n-gons in the Euclidean plane, having sides of length a
1,...,a
n
(in some order). The infimum is attained (in limit) if the polygon degenerates into a certain kind of triangle, plus some
parts of zero area. We show the same result for simple polygons on the sphere (of not too great length), and for simple polygons
in the hyperbolic plane. Replacing simple n-gons by convex ones, we answer the analogous questions. The infimum is attained also here for degeneration into a certain
kind of triangle.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
20.
Conclusion Long-term strength tests of textolite were conducted for seven different particular cases of the plane stressed state. Maximum times to failure for which experimental data were obtained reach 2500 h. It is established from analysis of the test results that the experimental long-term strength curves for the types of stressed state under consideration are closely similar. The condition of long-term strength in the general case of the plane stressed state for constant levels of stresses is taken as the equation of the short-term strength surface in which the time factor is introduced parametrically; in this case, the apparent observance of similarity between equilong-term strength surfaces makes it possible to express the tensor components characterizing the long-term strength by tensor components of the short-term strength surface and a certain monotonically decreasing time function, which is independent of the form of stressed state.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 51–56, January–February, 1979. 相似文献